...the second spring in the 65, as you said, is a light one that fits inside the much heavier mainspring. I've frankly never been convinced it did much of anything! And it seems to have come and gone in 65 production without much notice.
The double springs in the FWB 300S are a completely different concept. The action's main spring is in fact two short springs, which are wound in opposite directions, and which fit end-to-end inside the receiver. This idea was probably borrowed from the earlier Walther LGV target rifle--in fact, the spring assemblies for these two guns are interchangeable--the idea being to lessen the torque effect as the spring expands.
Walther didn't invent this concept either. The classic BSA underlevers first used such a spring more than 100 years ago!